Image scanner with a non-spherical fθ lens system

ABSTRACT

A laser printer includes a semiconductor laser for generating a laser beam which is modulated according to information, a rotating polygon mirror for scanning the laser beam generated by the semiconductor laser, and an fθ lens system for imaging, onto a photosensitive drum, the laser beam scanned by the rotating polygon mirror. The fθ lens system has first and second lenses arranged, in this order, next to the rotating polygon mirror and on the optical path through which the laser beam is introduced from the rotating polygon mirror to the photosensitive drum. Each of the first and second lenses has light-entering and -emerging faces which are formed in a non-spherical shape.

BACKGROUND OF THE INVENTION

The present invention relates to a recording apparatus such as the laserprinter.

In a laser printer as shown in FIG. 1, for example, laser beam Lgenerated by a laser generator (not shown) is scanned by rotatingpolygon mirror 2. This scanned laser beam L is introduced ontophotosensitive drum 12, via first fθ lens 4, first mirror 6, secondmirror 8, and second fθ lens 10, whereby the surface of drum 12 isexposed. Since the surface of photosensitive drum 12 has been previouslybeen charged by charger 14, an electrostatic latent image is formedthereon. In FIG. 1, numeral 16 denotes a means for developing theelectrostatic latent image to form a developed image, 18 a charger fortransferring the developed image onto a sheet of paper, 20 a means forfixing the transferred image on the sheet of paper, 22 a tray forreceiving the sheet of paper on which the image has been fixed, 24 acleaning means for removing the developing agent remaining onphotosensitive drum 12 after image transfer, 26 a lamp for removingelectricity from the surface of photosensitive drum 12 after thecleaning process has been completed, 28 a cassette for storing papersheets which are to be supplied between photosensitive drum 12 andtransfer charger 18, and 30 a guide for supplying the paper sheetsmanually.

First fθ lens 4 is spherical, while second fθ lens 10 is a toric. Eitherthe light-entering face or the light-emitting face of second lens 10 canbe formed having a toric face, this face being formed by rotating anarc. When the scanning angle of rotating polygon mirror 2 becomesgreater than ±30° in this case, the property of the fθ lens cannot besatisfied. The scanning angle which can meet the property of the fθ lensaccordingly becomes small. It is therefore needed that the optical pathextending from rotating polygon mirror 2 to photosensitive drum 12 ismade long for the purpose of making the scanning width large onphotosensitive drum 12. The apparatus thus becomes large in size andexpensive in cost.

SUMMARY OF THE INVENTION

The object of the present invention is to provide a recording apparatussmaller in size and lower in cost.

According to an aspect of the present invention, there is provided arecording apparatus for recording images on a recording medium, whichcomprises, means for scanning light modulated according to information,and an fθ lens system for imaging, on the recording medium, the lightscanned by the scanning means, the fθ lens system having first andsecond lens arranged next to the scanning means, in this order, and onthe optical path of the light introduced from the scanning means to therecording medium, each of these first and second lens havinglight-entering and -emitting faces each formed in a non-spherical shape.

According to the recording apparatus of the present invention, theproperty of the fθ lens can be fulfilled even when the scanning angle ismade equal to about ±45°. Therefore, the optical path extending from thescanning means to the recording medium can be made shorter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a sectional view showing the conventional laser printer.

FIG. 2 is a sectional view showing an example of the recording apparatusor laser printer according to the present invention.

FIG. 3 is a side view showing an exposure means in the laser printershown in FIG. 2.

FIG. 4 shows how the exposure means is arranged in the laser printer.

FIG. 5 shows laser and prism units in the exposure means.

FIG. 6 is a vertically-sectioned view showing the exposure means.

FIG. 7 shows the arrangement of an optical system in the exposure means.

FIG. 8 is a view intended to explain the shape of lens.

FIG. 9 is a front view showing a second fθ lens in FIG. 7.

FIG. 10 is a sectional view taken along a line A--A in FIG. 9 to showthe second fθ lens.

FIG. 11 is a sectional view taken along a line B--B in FIG. 9 to showthe second fθ lens.

FIG. 12 is a sectional view taken along a line C--C in FIG. 9 to showthe second fθ lens

FIG. 13 is a diagram showing the aberration correcting property (or fθproperty) of the first fθ lens.

FIG. 14 is a diagram showing the relationship between the curvature offield and the scanning angle in the case of the first fθ lens.

FIG. 15 is a diagram showing the aberration correcting property (or fθproperty) of the first and second fθ lens.

FIG. 16 is a diagram showing the relationship between the curvature offield and the scanning angle created by a luminous flux in the scanningface.

FIG. 17 is a diagram showing the relationship between the curvature offield of the scanning angle created by a luminous flux in a faceperpendicular to the scanning face.

FIG. 18 shows a variation of the second fθ lens.

FIG. 19 is a view intended to explain the shape of the second fθ lens inFIG. 18.

FIG. 20 shows another variation of the second fθ lens.

FIG. 21 is a diagram showing the relationship between the scanning angleand the spot size.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

FIG. 2 shows an example of the recording apparatus or laser printeraccording to the present invention. In FIG. 2, numeral 52 represents acasing. Photosensitive drum 54 which is rotated in a direction shown byan arrow is arranged in the center of casing 52. Exposure means 56 islocated below photosensitive drum 54 and it exposes photosensitive drum54 at a certain area thereof, which has been previously charged,according to image information to thereby form an electrostatic latentimage thereon. From the exposure region, the following are arranged:developing means 58 for developing the latent electrostatic image toform a toner image; transfer roller 60 for transferring the toner imagefrom photosensitive drum 54 onto paper sheet P; discharge lamp 62 forelectrically discharging photosensitive drum 54, to remove the surfacepotential therefrom; and charger 64 for uniformly charging the surfaceof photosensitive drum 54. These structural components are arranged inthe rotating direction of photosensitive drum 54 in the order mentioned.Paper sheet supply cassette 66 is detachably attached to the undersideof casing 52. Fixing means 68 is located in the upper portion of casing52. Paper sheets P in paper sheet supply cassette 66 are fed by roller70. Paper sheet P thus fed is aligned by aligning rollers 72. Papersheet P thus aligned is sent between a pair of rollers 74, passingthrough the transferring section and fixing means 68. The transferringsection is located between photosensitive drum 54 and transfer roller60. Fixing means 68 fixes the developed image onto paper sheet P. Papersheet P is discharged by rollers 74 onto tray 76 located in the upperportion of casing 52. Numeral 78 denotes a control means located betweenpaper sheet supply cassette 66 and tray 76 and this control means 78controls the whole of the printer.

The surface of photosensitive drum 54 is uniformly charged by charger 64when an image is to be formed. This charged photosensitive drum 54 isthen exposed by exposure means 56. An electrostatic latent image is thusformed on photosensitive drum 54. The developing agent is applied tothis electrostatic latent image by developing means 58, thereby makingthe electrostatic latent image visible. A developed image is thusformed. The developed image is then transferred onto paper sheet P bytransfer roller 60 at the transferring section. The developed imagewhich has been thus transferred onto paper sheet P is fixed on papersheet P by fixing means 68. Paper sheet P is then discharged onto tray76 by rollers 74. After the developed image is transferred onto papersheet P, the electrical potential on the surface of photosensitive drum54 is removed by lamp 62 and photosensitive drum 54 is thus made readyfor a next cycle of processes.

As shown in FIGS. 3 and 4, opening 80 is provided in the bottom ofcasing 52. Exposure means 56 is inserted into casing 52 through thisopening 80. Case 82 for exposure means 56 is provided with L-shapedgrooves 84 at both sides thereof and recess 86 at other side thereof.Casing 52 is provided with a pair of pins 88 engaged with grooves 84 andprojection 90 fitted into recess 86. When exposure means 56 is to beattached to casing 52, it is lifted, keeping its grooves 84 engaged withpins 88. It is thus inserted into casing 52 from below through opening80. When pins 88 reach the bottom of grooves 84, exposure means 56 isslid in the horizontal direction. When pins 88 come to the end ofgrooves 84, projection 90 of casing 52 is fitted into recess 86 of case82. Exposure means 56 is thus limited in its movement up and down and inits rotating direction. As the result, its position is determinedrelative to photosensitive drum 54. When it is positioned like this, itis fixed to casing 52 by means of screws 92 (FIG. 4). It can betherefore independently attached to and detached from casing 52. Inaddition, it can be held at a certain position even when screws 92 areunscrewed. Therefore, its incorporation into casing 52 can be easilyachieved and its position adjustment cannot be needed.

As shown in FIGS. 5 and 6, laser unit 94 is located on the top of case82 of exposure means 56. Semiconductor laser 96 and collimator lens 98are set integral to each other in laser unit 94. Semiconductor laser 96generates laser beam L which is modulated according to imageinformation. Laser beam L thus generated is paralleled by collimatorlens 98. Laser unit 94 freely rotates, taking the optical axis of laserbeam L emitted from semiconductor laser 96 (or optical axis of laserbeam L paralleled by collimator lens 98) as its rotation axial center.In addition, it is attached to case 82 in such a way that the opticalaxis of laser beam L emitted from semiconductor laser 96 becomessubstantially vertical to an optical scanning place between rotatingpolygon mirror 100 and first fθ lens 102 which will be described later.

As shown in FIG. 5, prism unit 104 is arranged in case 82. Prism unit104 includes two triangular prisms 106. Both ends of triangular prisms106 are held by holder member 110 through plate springs 108 in such away that apical angles of triangular prisms 106 are directed in a samedirection. Laser beam L which has been paralleled by collimator lens 98is made shorter only in a direction of its section and thus deflectedsubstantially at a right angle. Laser beam L therefore has anappropriate spot size on photosensitive drum 54. Holder member 110 isfreely rotatably fitted in opening 112 in case 82 and fixed at a desiredposition by screws 114. Therefore, the rotating position of holdermember 110 can be finely adjusted. Light emitted through triangularprisms 106 can be thus finely adjusted to head in a desired direction.

As shown in FIG. 6, scanning means 116 is located in case 82 andprovided with motor 118 which is mounted on the top of case 82. Shaft120 of motor 118 is projected downward and inclined. Rotating polygonmirror 100 is attached to shaft 120 and it scans laser beam L, which hasbeen deflected by triangular prisms 106, only by such a width thatcorresponds to the recording area of photosensitive drum 54. It isformed like a hexagonal column, having six reflecting faces 122 on itsside. It can scan laser beam L at a wide angle of about ±45°.

The distance from rotating polygon mirror 100 to photosensitive drum 54is 261 mm in the case of the conventional apparatus shown in FIG. 1 but258 mm in the case of the apparatus of the present invention. Theconventional apparatus is intended for paper sheets of A4 size and whenthey are scanned over a width of 210 mm with an fθ lens whose focaldistance f is 215 mm, therefore,θ=(1/2)×(210/f)(rad)=(1/2)×(210/215)×(180/π)=.+-.28°. The polygon mirroremployed by the conventional apparatus is therefore an octagonal columnhaving eight reflecting faces on its side. When the apparatus of thepresent invention is used for paper sheets of A3 size, a scanning angleof +41° is needed to scan them over a length of 297 mm using fθ lenssystem 126 whose effective focal distance f is 209 mm substantiallyequal to that in the conventional apparatus, becauseθ=(1/2)×(297/209)×(180/π)=±41°. This causes the apparatus of the presentinvention to use rotating polygon mirror 100 shaped like a hexagonalcolumn, as described above.

The fθ lens system 126 consisting of first and second fθ lenses 102 and124 is arranged together with first and second mirrors 128 and 130 incase 82. Second fθ lens 124 is located at the upper portion of case 82.Second mirror 130 is located adjacent to motor 118. Laser beam L scannedby rotating polygon mirror 100 is successively reflected by first andsecond mirrors 128 and 130 after passing through first fθ lens 102.Laser beam L reflected by second mirror 130 passes between rotatingpolygon mirror 100 and first fθ lens 102. After it passes through secondfθ lens 124, laser beam L is collected on photosensitive drum 54 andscanned in the width direction (or main scanning direction) ofphotosensitive drum 54. The width of first fθ lens 102 is determined insuch a way that the effective scanning angle is ±44°, for example. Sincefirst fθ lens 102 has a positive refractive index, the width of secondfθ lens 124 is set in such a manner that the effective scanning angle is+32°, for example. Third mirror 132 is located at one end of second fθlens 124 (see FIG. 4). This third mirror 132 reflects laser beam L,which has a scanning angle larger than ±32°, in a directionperpendicular to shaft 120 of motor 118. Laser beam L thus reflected isdetected by photoelectric converter element 134, which outputs a signalfor controlling the record starting position.

As shown in FIG. 7, light-entering and -emerging faces 102a, 124a and102b, 124b of first and second fθ lenses 102 and 124 are formednon-spherical.

First fθ lens has a positive refractive index. Light-entering face 102aof first fθ lens 102 is formed concave while its light-emerging face isformed convex. Second fθ lens 124 has first portion 124a1 including theoptical axis and second portion 124a2 including no optical axis.Light-entering and -emerging faces 124a and 124b of second fθ lens 124are shaped concave while second portion 124a2 thereof is formed convex.First portion 124a1 of second fθ lens 124 has a negative refractiveindex.

When their deflecting (or scanning) faces are denoted by plane y-z andtheir optical axis by axis z in the three dimensional coordinatesrelating to light-entering and -emerging faces 102a, 124a and 122b, 124bof first and second fθ lenses 102 and 124, the relationship betweenlevel z and distance y of the lenses on place y-z can be expressed by##EQU1## wherein RD represents radius of curvature, and AD, AE, AF andAG denote biquadratic, sextic, octal and decimal non-sphericalcoefficients in which |AD|+|AE|+|AF|+---.noteq.0.

When the curvature of light-entering face 102a is 1/(RD₁) and that oflight-emerging face 102b is 1/(RD₂) in the case of first fθ lens 102,##EQU2## When the face of lens is concave relative to the object (orsemiconductor laser 96), RE is negative.

Providing in the case of second fθ lens 124 that the curvature oflight-entering face 124a is 1/(RD₃) and that the curvature oflight-emerging face 124b is 1/)RD₄), ##EQU3##

Light-entering and -emerging faces 102a, 102b and 124a, 124b of firstand second fθ lenses 102 and 124 are formed similar to those which areformed when curves z obtained by the above-mentioned relationalexpressions are rotated round the optical axis (or axis z).

Light-emerging face 124b of second fθ lens 124 is formed toric. Thistoric face is obtained when curve z obtained by the above-mentionedrelational expressions is rotated round a straight line parallel to axisy and separated by z(=cvx) from the lens face on the optical axis (oraxis z).

AD, AE, AF and AG are in these ranges of |AD|<100/AP⁴, |AE|<100/AP⁶,|AF|<100/AP⁸ and |AG|<100/AP¹⁰, providing that the maximum radius oflenses is denoted by AP. These are such ranges that make coefficientsnot too large to orders or that make the lenses not too awkward inshape.

Providing that the junction of curve z relative to the optical axis (oraxis z) is denoted by z=0 and that the position of rotating axis byz=1/cvx in FIG. 8, an equation for expressing the toric face can beestablished from the above-mentioned expressions for curves z and fromthe expression of Z² +(1/cvx-z₁)² =(1/cvx-z)² that ##EQU4## Curves z arewithin plane y-z or beam deflecting plane (or scanning plane). They maybe shifted a little from plane y-z, considering light and the likestraying from photosensitive drum 54.

When the focal distance of combined first and second fθ lenses 102 and124 is denoted by f, the distance θ from light-entering face 102a offirst fθ lens 102 to that point of rotating polygon mirror 100 at whichlaser beam L is reflected is set to have a range of f/15-f/3. Thisdistance l is 30 mm, for example. When f=209 mm in this case,l/f=30/209=1/7.

In the case of first fθ lens 102, the distortion factor (y-fθ)/y(wherein y represents the beam position on the image field) of its fθproperty is set to be smaller 10%.

When the focal distance of combined first and second fθ lenses 102 and124 is denoted by f, the distance d from light-emerging face 125b ofsecond fθ lens 124 to the image field (or photosensitive drum 54) is setto be in a range of f/22-f/3. This distance d is 30 mm, for example.When f=209 mm in this case, d/f=30/209=1/7.

Second fθ lens 124 is arranged in such a manner that the amount ofcorrection relating to the curvature of field caused by the luminousflux in the deflecting (or scanning) face is about 0-30 mm.

First and second fθ lenses 102 and 124 are elongated rectangularparallelpipeds made of plastics such as acryl. Second fθ lens 124 isformed concave in section, as shown in FIGS. 9 through 12. Morespecifically, portion (used portion) 140 of second fθ lens 124 isconcaved in a direction along the optical axis except the rim portion ofits two opposite faces. Light-entering and -emerging faces 124a and 124bare formed at this used portion 140. Reinforcing portion 142 is formedaround used portion 140. Portions 144, recessed in section, are formedon those faces of second fθ lens 124 where light-entering and -emergingfaces are not formed.

According to the above-described arrangement, the following operationaleffects can be achieved.

(1) Light-entering and -emerging faces 102a, 124a and 102b, 124b offirst and second fθ lenses 102 and 124 are formed non-spherical. Evenwhen the scanning angle is made wide to have a value of ±45°, therefore,the fθ property can be fulfilled. The curvature of field can be thuscorrected. As the result, the apparatus can be smaller-sized and madelower in cost.

The modulation of semiconductor laser 96 is usually carried out inproportion to time. On the other hand, rotating polygon mirror 100rotates at a certain angular velocity. When paralleled laser beam Lentering into rotating polygon mirror 100 is considered as an infinitepoint, the height of this point is proportional to tan relating toincident angle θ of laser beam L into rotating polygon mirror 100. Laserbeam L reflected by rotating polygon mirror 100 is distorted by firstand second fθ lenses 102 and 124. Image height y which is proportionalto incident angle θ of laser beam L into rotating polygon mirror 100 canbe thus obtained. This image height y can be expressed like y=fθ(rad).First and second fθ lenses are formed so non-spherical as to make fcertain not as the focal distance but as factor of proportionality. Evenwhen the scanning angle is made wide, the fθ property can be fulfilled.

First fθ lens 102 is a non-spherical one having a positive refractiveindex. Light-entering face 102a of first fθ lens 102 is formed concavewhile light-emerging face 102b thereof convex. First fθ lens 102therefore shows such an fθ property as shown in FIG. 13. Further, firstfθ lens 102 causes a curvature of field. However, first portion 124a1 oflight-entering face 124a is formed concave while second portion 124a2 oflight-emerging face 124b convex in the case of second fθ lens 124. Firstportion 124a1 of second fθ lens 124 has a negative refractive index andsecond portion 124a2 thereof has a positive refractive index. Thispositive refractive index is small on those sided adjacent to and remotefrom the optical axis of second portion 124a2 but large in the centerthereof. Therefore, second fθ lens 124 can correct both of the fθproperty of first fθ lens 102 and the curvature of image field caused bythe luminous flux in plane y-z. Namely, the refractive index of first fθlens 102 becomes positive and that of first portion 124a1 of second lens124 becomes negative. Petzval curvature can be thus approximated to zeroas closely as possible. Even when the scanning angle is widened to about±45°, therefore, the fθ property can be fulfilled. At the same time, thecurvature of image field caused by the luminous flux in plane y-z can beprevented. Laser beam L can be thus scanned at a wide scanning angle.The optical path extending from rotating polygon mirror 100 tophotosensitive drum 54 can be shortened accordingly. The apparatus canbe thus smaller-sized and made lower in cost. Further, resolution can beenhanced because paralleled laser beam L can be collected ontophotosensitive drum 54 on plane y-z.

Light-emerging face 124a of second fθ lens 124 is formed toric.Therefore, the curvature of image field or tilting toward axis x (or inthe sub-scanning direction) caused by the luminous flux in a sectionperpendicular to plane y-z can be corrected, independently of thecorrection of the curvature of image field on place y-z. Even in thecase where reflecting faces 122 of rotating polygon mirror 100 areslanted because of the influence of working accuracy and the like, laserbeam L can be collected on plane y-z. Namely, the image field aftercorrecting the tilting in the sub-scanning direction can be madeconsistant with the focus or image field of paralleled laser beam onplane y-z.

The reflecting point on reflecting face 122 is moved by about 2 mm, forexample, following the rotation of polygon mirror 100. This movement ofthe reflecting point is done along the optical axis of incident laserbeam L. When reflected laser beam L is right-angled relative to incidentlaser beam L, therefore, the movement of reflecting point can beregarded as the movement of pupil. Even when the reflected point oflaser beam L moves on reflecting face 122, therefore, it is believedthat the position of image is left not influenced. However, the depth offocus which corresponds to the radius of incident laser beam L is neededas the optical system for correcting the tilting. When light-emergingface 124b of second fθ lens 124 which is formed toric is located as nearthe image (or photosensitive drum 54) as possible, the verticalmagnification becomes small and the depth of focus becomes largeaccordingly, thereby making it advantageous to correct the tilting. Theradius of beam which corresponds to the depth of focus needed as theoptical system for correcting the tilting is about ±2.5 mm.

(2) Light-entering and -emerging faces 102a and 102b of first fθ lens102 are formed non-spherical. In addition, the distance l fromlight-entering face 102a of first fθ lens 102 to that point onreflecting face 122 of rotating polygon mirror 100 where laser beam L isreflected is set to equal to f/15-f/3. The interval between rotatingpolygon mirror 100 and first fθ lens 102 can be thus so arranged thatlaser beam L reflected by second mirror 130 passes between them.

More specifically, when l=f/15=14 (mm), the interval between the outerend of rotating polygon mirror 100 and light-entering face 102a of firstfθ lens 102 becomes 2 mm. When it is smaller than 2 mm (l<1/15), laserbeam L reflected by second mirror 130 cannot be passed between rotatingpolygon mirror 100 and first lens 102. When l is made larger, first fθlens 102 is struck against first mirror 128. In addition, first andsecond fθ lenses 102 and 124 must be made longer and thicker. Therefore,more lens elements are needed and more time for forming and shaping themis also needed to thereby make the cost higher. Because of this designrequirement, l is preferably f/15 (l<f/15) at maximum.

The distortion factor (y-fθ)/y (wherein y represents the position ofbeam on image field) of fθ property is made smaller than 10% in the caseof first fθ lens 102. Both of the distortion caused by second fθ lens124 and the curvature of image field caused by the luminous flux in thedeflecting face can be thus corrected to a larger extent.

First fθ lens shows its original ability when it is combined with secondfθ lens 124. Unless the distortion is substantially corrected by firstfθ lens 102, however, both of the distortion and the curvature of imagefield cannot be corrected to the large extent. When the distortion issubstantially corrected by first fθ lens 102, therefore, second fθ lens124 can be used mainly to correct the curvature of image field. Thedistortion at first fθ lens 102 used was that (y-fθ)/y =8.7/164=5.3% atmaximum, as shown in FIG. 13.

(3) Light-entering and -emerging faces 124a and 124b of second fθ lens124 are formed non-spherical. These non-spherical shapes are such thatthe lens faces on plane y-z are expressed by the above mentioned curvesz. In addition, the distance d from light-emerging face 124b of secondfθ lens 124 to photosensitive drum 54 is set to equal to f/22-f/3.Sufficient tilting correction (or correction of the curvature of imagefield caused by the luminous flux in a section perpendicular to thescanning face) can be achieved. Further, no design problem is causedeven when it is arranged like this.

When second fθ lens 124 is separated too remote from photosensitive drum54, it is struck against motor 118. Further, the refractive indexbecomes small at the light-emerging toric face and the radius of beambecomes large in the sub-scanning direction (or direction along planey-z). Furthermore, when d is set larger than f/3, sufficient tiltingcorrection cannot be achieved. As d is made smaller, it is needed tomake the lens thicker and this is disadvantageous from the viewpoint ofmanufacture. When d is made smaller than f/22, for example, thethickness of the lens becomes larger than 25 mm. It is thereforepreferable to set d equal to f/22 -f/3.

Second fθ lens 124 is formed so that the curvature of image field causedby the luminous flux in the deflecting (or scanning) face can becorrected to an extent of about 0-30 mm. Sufficient tilting correctioncan be thus achieved.

As described above, first fθ lens 102 is intended mainly to correct thefθ property. The curvature of image field cannot be reduced accordingly.It is therefore needed that second fθ lens 124 have the relatively highability of correcting the curvature of image field. However, second fθlens 124 is intended to correct the fθ property a little and alsocorrect the tilting. This makes it difficult to give second fθ lens 124the high ability of correction. However, first fθ lens 102 enables thecurvature of image field to be made smaller than 30 mm. It may be enoughtherefore that the curvature of image field is corrected to an extent ofabout 0-30 mm only by second fθ lens 124. FIG. 13 shows the curvature ofimage field in the case of first fθ lens 102. The curvature of imagefield caused by the luminous flux in the scanning face is about 7 mm.This can be corrected by second fθ lens 124. The curvature of imagefield (or tilting) caused by the luminous flux in a face perpendicularto the scanning face is about 25 mm. This can be corrected mainly bylight-emerging toric face 124b of second fθ lens 124.

(4) First and second fθ lens 102 and 124 are formed non-spherical andmade of plastics. They can have a higher accuracy and be provided at alower cost accordingly.

The aberration property is excellently corrected by first and second fθlenses 102 and 124 at room temperature (or 15° C.), as shown in FIGS. 15through 17. Even when the refractive index of plastics is changed bytemperature, this refractive index is allowable.

First and second fθ lenses 102 and 124 are formed as elongatedrectangular parallelpipeds. The volume of first and second fθ lenses 102and 124 can be thus made small. The time of forming and shaping them canbe shortened accordingly. As the result, their manufacturing cost can belowered.

Second fθ lens 124 if formed concave in section. More specifically,portion (or used portion) 140 is concaved in a direction along theoptical axis, except the rim portion of two opposite faces of second fθlens 124. Light-entering and -emerging faces 124a and 124b are formed atthis used portion 140. They can be thus formed independent of eachother. The accuracy of forming and shaping them can be enhancedaccordingly.

Portions 144, recessed in section, are formed at that area of second fθlens 124 where its light-entering and -emerging faces 124a and 124b arenot formed. The time of forming and shaping second fθ lens 124 can bethus shortened without reducing the strength thereof. One minute isusually needed to process the thickness of 1 mm in the course of formingand shaping plastic lenses with high accuracy. Therefore, lenses as thinas possible are more advantageous in accuracy and cost. When they aremade too thin, however, they are likely to be warped. Used portion 140of second fθ lens 124 is formed at that area which is merely about 1 mmwide in the center portion of second fθ lens 124. Second fθ lens 124 istherefore provided with recess portions 144 to eliminate any additionalprocess of forming and shaping it. The time of forming and shaping itcan be thus shortened without reducing its strength.

(5) First and second mirrors 128 and 130 are located in such a way thatlaser beam L reflected by second mirror 130 can pass between rotatingpolygon mirror 100 and first fθ lens 102. The interval between rotatingpolygon mirror 100 and first mirror 128 can be thus made shorter, ascompared with the conventional apparatus (shown in FIG. 1) wherein laserbeam L passes between first fθ lens 102 and first mirror 128. The wholeof the optical system can be made more compact accordingly.

(6) Second mirror 128 is located adjacent to rotating polygon mirror100. The distance between first mirror 128 and rotating polygon mirror100 can be shortened accordingly. The whole of the optical system can bethus smaller-sized. Motor 118 is mounted on the top of case 82. Rotatingpolygon mirror 100 is attached to shaft 120 of motor 118, slanting andfacing downward. Even when second mirror 130 is located adjacent torotating polygon mirror 100, therefore, motor 118 does not become anobstacle against second mirror 128.

FIG. 18 shows a variation of the second fθ lens. Light-emerging face152a of this second fθ lens 152 is formed toric, having a certainrefractive index in its cut face when it is cut along a plane parallelto plane x-z. As shown in FIG. 19, it is a toric face, having a certainrefractive index independent of distance y. An equation of this toricface can be obtained from the expressions for the above-mentioned curvesz and from (z_(z) -z)² +x² =1/cvx² that ##EQU5## Light-entering 152a ofsecond fθ lens 152 is similar to light-entering face 124a of second fθlens 124.

According to this arrangement, working can be made easier when femalehalves of dies for molding plastics are made, particularly when lensesare polished.

FIG. 20 shows another variation of the second fθ lens. This second fθlens 162 is formed concave at light-entering face 162a thereof.Light-emerging face 162b of second fθ lens 162 is formed concave atfirst portion 162b1 thereof and convex at second portion 162b2 thereof.First portion 162b1 of second fθ lens 162 has a negative refractiveindex.

When the deflecting (or scanning) face is denoted by plane y-z and theoptical by axis z in the three-dimensional coordinates, light-enteringand -emerging faces 162a and 162b of second fθ lens 162 can be expressedby the following relational expression between the height of lens faceson place y-z and distance y: ##EQU6## wherein RD represents the radiusof curvature and Ad, AE, AF and AG denote biquadratic, sextic, octal anddecimal non-spherical coefficients in which |AD|+|AE|+|AF|+---.noteq.0.

When the curvature of light-entering face 162a is 1/(RD₃) and that oflight-emerging face 162b is 1/(RD₄), ##EQU7##

Light-entering face 162a of second fθ lens 162 has such a toric facethat is obtained when curve z expressed by the above-mentioned equationis rotated round an axis parallel to axis y and crossing axis z.

When light-emerging face 162b is formed toric, the radius of beam in thesub-scanning direction tends to become small where the angle of view islarge, as shown in FIG. 21. When light-entering face 162a is formedtoric, however, the radius of beam in the sub-scanning direction tendsto become large where the angle of view is large. The luminous energy ofbeam becomes smaller as the angle of view becomes larger. It istherefore preferable to make light-entering face 162a toric for thepurpose of making the size of images uniform on photosensitive drum 54.

What is claimed is:
 1. A recording apparatus for recording images on arecording medium, comprising:means for scanning light modulatedaccording to information; and an fθ lens system for imaging, on therecording medium, the light scanned by the scanning means, said fθ lenssystem having first and second lenses arranged, in this order, next tothe scanning means and on the optical path through which the light isintroduced from the scanning means onto the recording medium; said firstand second lenses having light-entering and light-emerging faces eachformed in a non-spherical shape; said second lens having a first areanear its optical axis with a negtive refractive index, and a second areafarther from the optical axis than the first area with a positiverefractive index.
 2. The recording apparatus according to claim 1wherein said first lens has a positive refractive index, one of thelight-entering and -emerging faces of said first lens is formed concavewhile the other thereof is formed convex, said second lens has a firstarea including an optical axis and a second area including no opticalaxis, and the light-entering and -emerging faces of said second lens areformed concave at the first area thereof while they are formed convex atthe second area thereof, thereby allowing the first area to have anegative refractive index.
 3. The recording apparatus according to claim2, wherein provided that the curvature of the light-entering face isdenoted by 1/(RD₁) and the curvature of the light-emerging face isdenoted by 1/(RD₂) in the case of said first lens, in the followingrelational expression between the height of a lens and a distance y on aplane y-z in the three-dimensional coordinates; ##EQU8## wherein RDrepresents the radius of curvature, and AD, AE, AF, and AG denotebiquadratic, sextic, octal, and decimal non-spherical coefficients inwhich |AD|+|AE|+|AF|+---.noteq.0, a relation can be obtained wherein##EQU9## and provided that the curvature of the light-entering face isdenoted by 1/(RD₃) and the curvature of the light-emerging face isdenoted by 1/(RD₄) in the case of said second lens, in theabove-mentioned relational expression, a relation can be obtainedwherein ##EQU10##
 4. The recording apparatus according to claim 3,wherein the light-emerging face of said second lens has such a toricface as is obtained when the curve z expressed by the above-mentionedrelational expression is rotated round a certain axis parallel to theaxis y and crossing the axis z.
 5. The recording apparatus according toclaim 1, wherein said first lens has a positive refractive index, one ofthe light-entering and -emerging faces of said first lens is formedconcave while the other thereof is formed convex, and said second lenshas a first area including an optical axis and a second area includingno optical axis, one of the light-entering and -emerging faces of saidsecond lens is formed concave while the other thereof is formed concaveat the first area and convex at the second area, thereby allowing atleast the first area to have a negative refractive index.
 6. Therecording apparatus according to claim 5, wherein provided that thecurvature of the light-entering face is denoted by 1/(RD₁) and thecurvature of the light-emerging face is denoted by 1/(RD₂) in the caseof said first lens, in the following relational expression between theheight of a lens face and a distance y on a plane y-z in thethree-dimensional coordinates; ##EQU11## wherein RD denotes the radiusof curvature, and AD, AE, AF, and AG represent biquadratic, sextic,octal, and decimal non-spherical coefficients in which|AD|+|AE|+|AF|+---.noteq.0, a relation can be obtained wherein ##EQU12##and provided that the curvature of the light-entering face is denoted by1/(RD₃) and the curvature of the light-emerging face is denoted 1/(RD₄)in the case of said second lens, in the above-mentioned relationalexpression, a relation can be obtained wherein ##EQU13##
 7. Therecording apparatus according to claim 6, wherein the light-enteringface of said second lens has such a toric face as is obtained when thecurve z expressed by the above-mentioned relational expression isrotated round a certain axis parallel to the axis y and crossing theaxis z.
 8. The recording apparatus according to claim 6, wherein atleast one of the light-entering and -emerging faces of said second lenscan be expressed by the following relational expression between theheight of a lens and a distance y on a place y-z in thethree-dimensional coordinates; ##EQU14## wherein RD denotes the radiusof curvature, and AD, AE, AF, and AG represent biquadratic, sextic,octal, and decimal non-spherical coefficients in which|AD|+|AE|+|AF|+---.noteq.0, and the curvature at a section parallel to aplane x-z is certain independently of the distance y.
 9. The recordingapparatus according to claim 1, wherein said non-spherical faces can beexpressed by the following relational expression between the height z ofa lens and a distance y on a plane y-z in the three-dimensionalcoordinates; ##EQU15## wherein RD denotes the radius of curvature, andAD, AE, AF, and AG represent biquadratic, sextic, octal, and decimalnon-spherical coefficients in which |AD|+|AE|+|AF|+---.noteq.0, andprovided that the maximum radius of lens is denoted by AP, thenon-spherical coefficients are in ranges of|AD|<100/(AP)⁴,|AE|<100/(AP).sup.6, |AF|<100/(AP)⁸, |AG|<100/(AP)¹⁰,---.
 10. The recording apparatus according to claim 1, wherein saidfirst and second lenses are made of plastics.
 11. The recordingapparatus according to claim 10, wherein said first and second lensesare formed as elongated rectangular parallelepipeds.
 12. The recordingapparatus according to claim 10, wherein at least one of said first andsecond lenses is provided with recesses at that portion thereof throughwhich the light travelling from the scanning means to the recordingmedium cannot pass.
 13. The recording apparatus according to claim 1,wherein when the focal distance of said fθ lens system is denoted by f,the distance from the light-entering face of said first lens to thelight-emerging point of said scanning means is in a range of f/15-f/3.14. The recording apparatus according to claim 13, wherein said firstlens has such an fθ property that the distortion factor (y-fθ)/y can bemade smaller than 10% when the position of luminous flux on the imagefield is denoted by y.
 15. The recording apparatus according to claim 1,wherein when the focal distance of said fθ lens system is denoted by f,the distance from the light-emerging face of said second lens to theimage field is in a range of f/22-f/3.
 16. The recording apparatusaccording to claim 15, wherein said second lens has such an fθ propertythat the curvature of image field in the scanning face caused by theluminous flux which has been scanned by the scanning means can becorrected to an extent of 0-30 mm.